Officials have already begun counting votes, though most observers say victory is too close to call, with the outcome set to hinge on which man voters most trust to revamp an economy still struggling to recover from a 2016 recession.
Some analysts say the postponement is likely to harm both parties equally, as their supporters who had travelled home to vote last week will be unable to make another journey this weekend.
Despite the record number of registered voters, militant group Boko Haram warned people not to cast their ballots.
Buhari brushed aside reporters' questions about whether he would accept a loss to top challenger Atiku Abubakar, a billionaire former vice president.
According to Sahara Reporters, residents of Maiduguri are now in panic as series of explosions have rocked the city all within ten minutes.
The army also confirmed a "futile" attack on a security outpost in Geidam in Yobe state.
Observers said the delay of the election from last week, blamed on logistical challenges, could favor Buhari and the ruling party, with some Nigerians saying they didn't have the resources to travel to their place of registration a second time.
Nigeria's Business Day newspaper on Friday said whoever wins has to fix a "broken economy" limping back from recession, and hit by high unemployment, inflation and weak growth.
"There are some areas that need some attention especially on the delay in the time of commencement of voting".
Gunfire also was heard in Port Harcourt in Nigeria's restive south, where the military presence was heavier than in past elections.
"So far, I think we are asking the people of Nigeria as the largest democracy in Africa, to perform their civic responsibility by voting".
Buhari, voting in his northern hometown of Daura, jokingly checked the ballot his wife was casting to see whom she had voted for. Why did they have to come without the result sheet?
Boko Haram's Islamist insurgency in northeast Nigeria has killed more than 27,000 people and left 1.8 million people homeless.
The Independent National Electoral Commission (INEC) has assured Nigerians and the global community that it has concluded arrangements to commence elections by 8. a.m. on Saturday.
TV3's correspondent stationed in the federal capital of Abuja, Komla Klutse, said poor visibility could affect results.
On Saturday, Buhari responded to journalists asking if he would accept defeat and congratulate the victor if he loses: "I will congratulate myself", he said laughingly.
There were also sporadic incidents of snatching election materials, said police spokesman Nnamdi Omoni.